Crossword Genius

Anxious to have a cut? (4)

Ross

I believe the answer is:

keen

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'anxious' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

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(Other definitions for keen that I've seen before include "Fierce - sharp" , "moan" , "Eager; dirge" , "Quick" , "devoted" .)

I've seen this clue in the Evening Standard.
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